ABSTRACT
In this chapter we shall present a Morse Theory for the geodesies on a stationary Lorentzian manifold. Let f : M → R be a smooth functional on a Hilbert manifold M and let p be a critical point of f. In section 5.2 we shall define a bilinear form on TpM, the Hessian f"(p) of f at the point p. The Morse index of p is the maximal dimension of a subspace of TpM on which f"(p) is negative definite.
